In this section we apply the methodology presented in Sections  and  to real data in order to evaluate and compare its empirical implications with the ones obtained by using a univariate framework. Particularly, we follow [1]} and use weekly returns of the FTSE 100, NIKKEI 225, and S&P 500 stock market indices, from April 26, 1985 to February 01, 2021. Using a rolling window exercise, we estimate the one-week-ahead VaR and ES forecasts implied by the CAViaR specifications described in Section REF , and select the most desirable model using the [2]} test.
In a second empirical exercise, we aggregate the market indices to form a financial portfolio and determine its optimal allocation weights by solving the optimization problem described in Section REF . We finally compute and assess the resulting portfolio's conditional VaR and ES for the out-of-sample period, which consists of the last 368 observations of the sample.
